The Farrell-Jones Conjecture for mapping class groups

• 成果类型: Article
• 署名作者: Bartels, Arthur; Bestvina, Mladen
• 署名单位: University of Munster; Utah System of Higher Education; University of Utah
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0834-9
• 发表日期: 2019
• 页码: 651-712
• 关键词: uniform hyperbolicity; intersection-numbers; curve complex; K-THEORY; geometry; foliations; dimension; geodesics; BOUNDARY; lattices

摘要

We prove the Farrell-Jones Conjecture for mapping class groups. The proof uses the Masur-Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmuller space. The proof is presented in an axiomatic setup, extending the projection axioms in Bestvina et al. (Publ Math Inst Hautes Etudes Sci 122:1-64, 2015). More specifically, we prove that the action of on the Thurston compactification of Teichmuller space is finitely F-amenable for the family F consisting of virtual point stabilizers.